|The basic evolution of a spring snowmelt cycle in the West seems to start with a change in atmospheric circulation. A low pressure (winter) pattern is replaced (within days) by a strong and expanding high-pressure pattern, accompanied by high air temperature and a persistent surge in snowmelt-driven discharge (Cayan, in this issue). This, at least for purposes of discussion, might be called a hydroclimatic spring transition (Fig. 4), upper panel. This transition may or may not show a relation to the presumably more fickle (?) oceanographic/atmospheric spring transition (c.f., Strub et.al, 1988, for a discussion of the oceanographic spring and fall transition).
Following the typical strong surge in discharge, the temperature response coefficients (bi) in equation (1) largely track the rise in discharge as temperature increases its control over the snowmelt process. At some point the system is saturated (the rise in coefficients tends to flatten out). This phase is followed by a steady decline. This point of the decline, where the sum of the coefficients (or gain) decreases, might be a summer transition (Fig. 4, lower panel we are not aware of an oceanographic counterpart summer transition).
The initial stages of forecasting spring snowmelt discharge using statistical-dynamical time series are encouraging. These methods provide some insight into the response characteristics of the system, but we need to test further the forecasting power in our data-derived coefficients (cf., Dettinger, this issue). We know the coefficients vary from year-to-year and tend to be higher in wet than in dry years. The alternating use of a Kalman filter with the difference equation appears to extend forecasts beyond low risk 1-day forecasts which use only observed discharge values. Also, multi-parameter models such as input of the daily variations in high-elevation snowpack as well as air temperature, may better constrain predictions, but such records are short. As the model complexity increases, it makes more sense to use physically-based models (Jeton and Smith, 1993; Jeton et.al, 1996). In closing, we have only scratched the surface, and, as you can see (Fig. 6), there are many options.
Figure 6. Cartoon of an overjoyed (overwhelmed?) scientist pondering which method to select next in time series analysis of the atmospheric - hydrologic system.
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